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Due to active actions of groundwater and geothermal, the stability of underground engineering is important during geological structure active area. The damage mechanical theory and statistical mesoscopic strength theory based on Weibull distribution are widely used to discuss constitutive behaviors of rocks. In these theories, a statistical method is used to capture mesoscopic properties of rocks in order to generate a realistic behavior at a macroscopic scale. Based on the above theories, this paper aims at establishing a constitutive relation of brittle rocks under thermal-mechanical coupling conditions. First, a statistical damage constitutive model was established by considering the thermal effects and crack initiation strength. Subsequently, the parameters of the model were determined and expressed according to the characteristics of stress-strain curve. Third, the model was verified by conventional triaxial experiments under thermal-mechanical actions, and the experimental data and theoretical results were compared and analyzed in the case study. Finally, the physical meaning of the parameters and their effects on the model performance were discussed.

The three-parameter Weibull distribution has a strong ability to fit many kinds of experimental data, which provides a solution for using a unified expression to characterize the elastic-brittle, strain softening, elastic-plasticity, and other constitutive behaviors of rocks. Therefore, a statistical damage constitutive model based on three-parameter Weibull distribution was constructed through theoretical analysis and derivation. Its expression ability was verified by combining with the conventional triaxial compression test data of marble. Meanwhile, the application effect of this statistical damage constitutive model on granite and sandstone was analyzed. The results show that the statistical damage constitutive model of rock based on three-parameter Weibull distribution can well express elastic-brittle, elastic-plastic, strain softening behaviors of rock by setting reasonable constitutive parameters, which lays a theoretical foundation for constructing a unified rock constitutive model. Conventional triaxial tests of marble show that with the increasing of confining pressure (σ3= 5, 15, 25, 35 MPa), the plastic deformation increases and the failure mode gradually changes from brittle tensile failure to shear failure, showing brittle-ductile and brittle-plastic transition characteristics. And its constitutive behaviors are characterized by elastic-brittleness, strain softening, and elastic-plasticity, which can be well expressed by the statistical damage constitutive model. When σ3 is 25 and 35 MPa, sandstone samples show elastic-brittle behavior. And for granite samples, they show strain softening behavior when σ3 is 5 MPa. The statistical damage constitutive model is also suitable for describing both sandstone elastic-brittle behavior and granite strain softening behavior. It is concluded that the three-parameter Weibull distribution provides a useful approach to characterize various constitutive behaviors of rock, and the model has a wide potential in numerical simulation for mining engineering, geoengineering, and other rock engineering.

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